Heavy support command beacon seems really strangly worded and confusing to me. Do you do it When revealing an order marker or after taking a turn, which is it? These are opposite ends of a turn.

You only do it after taking a turn. The "when revealing an Order Marker" part is just there to specify that you have to have revealed on Order Marker on him to be able to take that extra turn, so no bonding with Zettian Infantry or Ornak to get the free turns.